Solve for $x$ and $y$ using elimination. ${3x+y = 14}$ ${2x-y = -4}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $5x = 10$ $\dfrac{5x}{{5}} = \dfrac{10}{{5}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {3x+y = 14}\thinspace$ to find $y$ ${3}{(2)}{ + y = 14}$ $6+y = 14$ $6{-6} + y = 14{-6}$ ${y = 8}$ You can also plug ${x = 2}$ into $\thinspace {2x-y = -4}\thinspace$ and get the same answer for $y$ : ${2}{(2)}{ - y = -4}$ ${y = 8}$